The Supreme Court is already seized of the matter with more than 60 petitions challenging the law and a hearing on the matter is scheduled on January 22.
The Left-led Kerala government in the petition termed the new law violative of several Articles in the Constitution, which includes right to equality, and cited that this law is against the basic principles of secularism enshrined in the Constitution.
The Kerala government urged the apex court to pass a judgement declaring the law to be ultra vires the Constitution and void.
The state government has also challenged the validity of changes made in 2015 to the Passport law and the Foreigners (Amendment) Order.
Meanwhile, a plea has also been filed in Supreme Court seeking directions to declare the CAA constitutional and also the Election Commission to identify and take stern action against the political parties spreading false rumours in the country.
The PIL, filed by Mumbai-based Puneet Kaur Dhanda through lawyer Vineet Dhanda, is the first in the apex court supporting Centre's legislation and sought a direction to declare the CAA as "constitutional" saying that this law should be implemented by states aggressively.
The law provides citizenship to non-Muslim migrants belonging to Hindu, Sikh, Buddhist, Christian, Jain and Parsi communities who had come into the country from three countries - Pakistan, Bangladesh and Afghanistan - on or before December 31, 2014.
On December 18, a bench comprising Chief Justice S.A. Bobde and Justices B.R. Gavai and Surya Kant refused to grant a stay on the implementation of the law and listed the matter for further hearing in January. The court issued notice to the Centre. All the matters will be heard together by the apex court on January 22.
Kerala government said the CAA violates the constitution and strikes at the root of India's secular and democratic principles. Recent resolution passed by the state Assembly against CAA has been attached with the petition.
( With inputs from IANS )